'Scientists think that chemical exposure, dietary habits and environmental factors may all have epigenetic affects'. Does that not mean that someone cannot be identified by DNA because it is variable over time. That article basically says that the genome trace of two identical twins is more different if they are older.

I think that it's not so much differences in the DNA, but where and how much the DNA is methylated. That is, where a methyl group (CH3) is added to the DNA. And from that article the scientists plan on figering out how DNA is methylated.

It is not quite true that DNA doesn't change during a persons life (if it didn't there would not be cancer). However, for practical purposes you can assume that if you take a sample of DNA from a person now and again in 20 years that they will be identical. This is because a persons genetic profile is constructed from many thousands to millions of copies of each DNA fragement so that any mutations in any one cell are averaged out.

Yea - exposure under the sun might result in alterations in DNA. Alterations in our DNA in our lifetime range from point mutations, to thymine dimers and etc..then again, there're also carcinogens and polyomaviruses?

It is possible to find differences in identical twins if the mitochondrial DNA is tested.
In addition, the expression of genes in monozygotic twins can be different. For example, a minor infection can trigger the genes that code the immune system to respond in different ways, resulting in different antibody protein molecules to be found in each twin. Mutations and rearrangement of pieces of DNA can slightly change as the twins grow, causing differences.